Mathematical Learning Environments Research Articles

Mathematical literacy learning environment for inclusive education teachers: A framework

The Program for International Student Assessment (PISA) 2022 study revealed low mathematical literacy scores among students, including those in inclusive education settings. A significant factor contributing to this issue is the inadequate capacity of teachers to effectively teach mathematical literacy. In response, this study aimed to design a mathematical literacy learning environment framework to enhance teachers' theoretical and practical understanding of teaching mathematical literacy in schools. The research employed a design research methodology, specifically the development study type, which involved preliminary research, prototype development, and evaluation stages. This paper focuses on the preliminary research phase, where data were collected through literature reviews and focus group discussions (FGDs) with teachers from inclusive schools. The collected data were analyzed qualitatively and descriptively. The study successfully developed a framework for a mathematical literacy learning environment that integrates courses, social media, and community engagement. This framework is intended to serve as a comprehensive reference for improving teachers' capacity to teach and assess students' mathematical literacy in a more holistic manner.

Innovative Teaching Techniques for Alleviating Mathematics Phobia Among Secondary School Students in Anambra State

This study explores innovative teaching techniques to address mathematics phobia among secondary school students in Anambra State. Recognizing the pervasive impact of mathematics anxiety on academic performance and psychological well-being, the research focuses on the efficacy of two innovative approaches: inquiry-based learning and peer teaching. The study involves 50 secondary school students and employs a self-designed questionnaire validated by mathematics department lecturers, a measurement and evaluation expert, and an experienced secondary school teacher. Data collection was conducted through an online survey designed using Google Forms, providing a convenient and efficient method for participants to respond. Results from the online survey reveal insights into the comparative effectiveness of these techniques, highlighting gender-specific variations. Notably, peer teaching emerged as a more favorable technique. The slightly higher variability in scores in the peer teaching method, as indicated by the standard deviation, suggests that while it may lead to higher average performance, it also introduces greater variability, emphasizing the need for tailored approaches to accommodate diverse learning styles. The study contributes localized data to the broader literature, addressing gaps in understanding mathematics phobia in Anambra State. Findings aim to inform educators, policymakers, and practitioners about evidence-based strategies to create a positive and inclusive learning environment for mathematics in secondary schools.

When algebra makes you smile: Playful engagement with early algebraic practices

BackgroundThe typical competitive and results-driven approach to school mathematics has traditionally been conceived as devoid of play, joy, and positive affect. AimsIn this paper we address the following questions: What markers of positive affect are observed while students are doing early algebra? Specifically, how are students’ markers of joy related to early algebraic practices? What are the characteristics of playful stances to learning early algebra that are observed when children express positive epistemic affect? SampleWe analyze three cases in which elementary school students engaged in tasks from an early algebra classroom teaching experiment. MethodsDrawing from two theoretical frameworks, epistemic affect and early algebra, we conducted microgenetic analyses of lesson transcripts to identify markers of joy and early algebraic practices. We conducted frequency analyses to determine their co-occurrence. ResultsOur results indicate that children expressed joy while engaging in early algebraic practices, evidence of positive epistemic affect. We describe the aspects of each of the cases we present in terms of prior literature on playful stances to learning to further bolster our claims about the relationship between joy and engagement with the early algebraic practices. ConclusionsWe conclude that mathematical learning environments should include open opportunities for students to engage with mathematical content, with multiple entry points and ways to respond. We also conclude that early algebraic practices provide opportunities for playfully engagement and positive epistemic affect.

LEPscO: Mathematical literacy learning environment for the Guru Penggerak program

LEPscO: Mathematical literacy learning environment for the Guru Penggerak program

STEAM practices connecting mathematics, arts, architecture, culture and history in a non-formal learning environment of a museum

This study adopts STEAM practices integrating architecture, arts, culture, and history into mathematics education in a museum learning environment. A workshop was conducted with five in-service mathematics teachers in an Egyptian museum, utilizing digital technologies such as GeoGebra, Augmented Reality, and 3D Printing to model, visualize and connect the museum collections to their teaching practices. Teachers’ modelled artefacts were qualitatively analysed for their artistic, cultural and historical connections. Findings indicate that participants followed the design expected outcomes of these STEAM practices by implementing a transdisciplinary approach towards mathematically modelling the museum objects while connecting to their mathematical, cultural, historical, and artistic relations. Participants’ reflections showed positive changes in their attitudes towards considering the museum learning environment for mathematics teaching during the implementation of these STEAM practices. Furthermore, such STEAM practices allowed participants to explore and connect disciplines through interacting with museum collections from artistic, cultural, historical, mathematical, and technological perspectives.

Flipped Classroom; Inovasi Pengaturan Lingkungan Belajar dalam Pembelajaran Matematika

Innovation in learning can be done by changing the paradigm of mathematics teaching and inspiring teachers to provide alternative learning environment settings and gain new experiences. The flipped classroom (FC) is currently an innovative pedagogical approach that has the opportunity to transform mathematics learning in the future. The tasks given by teachers, teacher feedback and scaffolding, as well as the changing teaching and learning environment at FC provide a new paradigm for mathematics teachers in learning to meet student characteristics that are different from previous times. The aim of this research is to theoretically and conceptually reveal the Flipped Classroom as a learning environment setting in mathematics learning with a blended form of learning that reverses the traditional classroom learning environment by delivering teaching content, via video or other sources outside the classroom. This research uses a conceptual literature review with a descriptive approach. FC-based learning environment settings, students will watch learning material via videos on online platforms or other, students can collaborate in discussions or individually, or carry out experiments at home and be actively involved in applying concepts in the classroom guided by a teacher. Well-designed FC offers great opportunities to improve students' mathematical thinking and understanding. In this regard, FC is recommended for teachers to use as a setting for a mathematics learning environment in the future, which is appropriate to the characteristics of students in the digital era.

Matematik Öğretiminde Okul Dışı Öğrenme Ortamları Dersinin Öğretmen Adaylarının Düşüncelerine Etkisi

In this study, it was aimed to determine the self-efficacy beliefs of pre-service elementary mathematics teachers towards out-of-school learning (OoSL) activities and their thoughts about out-of-school learning environments (OoSLE) before and after the out-of-school learning environments in mathematics teaching course. In line with this purpose, the effect of out-of-school learning environments course in mathematics teaching taught at undergraduate level was examined. In the study, a mixed research method model was adopted. The participants of the study consisted of 59 elementary mathematics teachers candidates studying in the 4th grade at a state university in Türkiye. "Teacher Self-Efficacy Beliefs Scale for Out-of-School Learning Activities" and six open-ended questions about out-of-school learning environments were used as data collection tools. It was concluded that the out-of-school learning environments course in mathematics education had a positive effect on pre-service teachers' self-efficacy and their thoughts about out-of-school learning.

Personalization in Graphically Rich E-Learning Environments for K-6 Mathematics

This report describes a randomized controlled study that compared personalization of educational content based on neural networks to personalization by human experts. The study was conducted in a graphically rich online learning environment for elementary school mathematics, in which N = 135 fourth- and sixth-grade students learn via mathematical applets. The performance of students who followed the algorithm's recommendations was compared to that of students who followed an a-priori sequence constructed by the experts. While the algorithm only considered students' performance on past problems when recommending new problems, the human experts also took into consideration other factors related both to content and to the graphical interface. The findings reveal no significant differences in performance between the two groups, suggesting that the algorithm was as successful in preparing the students as human teachers. Herein we discuss the different mechanisms used to prepare each of the groups for the learning tasks and highlight the importance of the user interface in that process. Specifically, we find that applets involving supportive interactions, in which students' interactions were intended to help solve the problem but were optional, represented students' pre-knowledge, while applets entailing required interactions did not. We contribute to the field of personalization in education with new evidence of the advantages of a content sequencing algorithm—based on collaborative filtering ranking and implemented via a neural network—in a graphically rich environment as tested in authentic classrooms.

Assignment strategies modulate students' academic performance in an online learning environment during the first and second COVID-19 related school closures.

A growing number of studies seek to evaluate the impact of school closures during the ongoing COVID-19 pandemic. While most studies reported severe learning losses in students, some studies found positive effects of school closures on academic performance. However, it is still unclear which factors contribute to the differential effects observed in these studies. In this article, we examine the impact of assignment strategies for problem sets on the academic performance of students (n ≈ 16,000 from grades 4-10 who calculated ≈ 170,000 problem sets) in an online learning environment for mathematics, during the first and second period of pandemic-related school closures in Germany. We observed that, if teachers repeatedly assigned single problem sets (i.e., a small chunk of on average eight mathematical problems) to their class, students' performance increased significantly during both periods of school closures compared to the same periods in the previous year (without school closures). In contrast, our analyses also indicated that, if teachers assigned bundles of problem sets (i.e., large chunks) or when students self-selected problem sets, students' performance did not increase significantly. Moreover, students' performance was generally higher when single problem sets were assigned, compared to the other two assignment types. Taken together, our results imply that teachers' way of assigning problem sets in online learning environments can have a positive effect on students' performance in mathematics.

Influence of primary students' self-regulated learning profiles on their rating of a technology-enhanced learning environment for mathematics.

The importance of learning technologies for mathematics education is increasing as new opportunities arise for mathematics education for all students, in school and at home. These so-called technology-enhanced learning environments (TELEs) incorporating technology with mathematical content are useful for developing mathematical knowledge and can simultaneously foster self-regulated learning (SRL) and motivational learning in mathematics. However, how do primary students' differences in their SRL and motivation affect their rating of the quality of mathematical TELEs? To answer this research question, we asked third and fourth-grade primary students (n = 115) to evaluate both their SRL, including metacognition and motivation, and the quality characteristics of the ANTON application, a frequently and intensively used TELE in Germany. Using a person-centered research approach by conducting a cluster analysis, we identified three SRL profiles of primary students-motivated self-learners, non-motivated self-learners, and average motivated non-self-learners-who differ in their ratings of the quality characteristics of the TELE (output variables). Our results highlight that motivated self-learners and non-motivated self-learners vary significantly in their rating of the adequacy of the TELE to their mathematical learning and highly but not significantly concerning the TELE's reward system. Moreover, differences existed between the motivated self-learners and the average motivated non-self-learners regarding their rating of the characteristic differentiation. Based on these findings, we assume that technical elements associated with adequacy, differentiation, and rewards of mathematical TELEs should be tailorable to the needs of individuals and groups of primary schoolchildren.

ZPD Technological Learning Environment In Learning Computational Thinking Skill-Based Mathematics

This research was conducted as an innovation related to learning problems that often occur in students. This research aims to develop a technological prototype of the mathematics-computation learning environment for playing skills using the Zone of Proximal Development (ZPD) approach based on intelligent technology. This type of research is Research and Development using the 4-D model flow (Four-D Models). The sampling technique is purposive sampling. Data collection in this study uses angles for learning environment data sources and computational thinking. Then interviews are used as a source of learning experience data. Data analysis on quantitative data types used descriptive and inferential statistics in the form of independent sample t-tests and the Miles and Huberman model. This study found differences in the computational thinking abilities of male and female students, and the dominant computational thinking abilities were male students. This development research has produced an online learning environment product where the product is valid in the opinion of experts in the good category, exciting and feasible to implement. The learning environment assists and facilitates students in learning mathematics by using technology geared toward improving thinking.

Relationship between Parents’ Beliefs in Early Mathematics and Learning Environment Provision at Home

Mastering early mathematics is crucial for young children's development and future, and parents' beliefs in early mathematics development and learning environment provision at home have been identified as factors that affect children's mathematical mastery. This cross-sectional survey study was conducted to examine the relationship between the level of parents' beliefs in early mathematics and learning environment provision at home. Two adapted structured questionnaires were used for data collection, namely, parents’ beliefs in early mathematics, and learning environment provision at home. The questionnaire was distributed online using the Google form platform and a total of 478 respondents completed it. Later, data were analyzed using the Statistical Program Package for Social Science through inferential statistics (Pearson's correlation coefficient test). Findings indicated that there was a weak, significant, positive relationship between the level of parents' beliefs in early mathematics and learning environment provision at home. These findings proved that parents’ belief in early mathematics was positively associated with provision of a learning environment at home. The increase in the level of parents’ belief in early mathematics is associated with increases in the learning environment provision at home. Therefore, support programs or workshops can be provided to parents to increase their knowledge of how to provide an appropriate, comprehensive and effective learning environment at home. These efforts, in turn, may help children to do well in mathematics.

The Relationship between Students' Mathematics Learning Environment, Attitude and Achievement: A Mediation Model

The Relationship between Students' Mathematics Learning Environment, Attitude and Achievement: A Mediation Model

INVESTIGATION OF THE EFFECTIVENESS OF PERSONALIZED ADAPTIVE MATHEMATICS TEACHING

The study aimed to empirically investigate the effectiveness of personalized adaptive learning in mathematics. To clearly explain this approach, we have deeply analyzed and used a mixed methodological approach to analyze satisfaction with the learning environment, perception, and attitude to the content provided, as well as general experience and personalized adaptive experience in the context of an electronic learning environment in mathematics. The students were distributed according to one of two conditions: an electronic learning environment known as personalized adaptive learning, and the same learning environment without the integration of a personalized adaptive learning platform. The necessity of using statistical methods for a reliable assessment of the results of experimental work in pedagogical research is considered, as well as the results of using two statistical criteria, and the difficulties that may arise during their implementation are analyzed on a practical example. To evaluate the effectiveness of adaptive personalized technologies, it was planned to use the Fisher criterion and the Student's t-criterion. They were chosen because they are based on two different types of scales: ordinal and interrelated.

Learning Mathematics through virtual mode: A review of literature

This paper identified the gap in existing literature in virtual learning environment in Mathematics. About seven books, twenty-nine journal articles, four conference papers and eight doctoral dissertations were collected from five different websites (Research gate, Elsevier, Wolfram Alpha, Directory of open access journals and Semantic scholar) and four electronic databases (Pro Quest Dissertations & Theses Global, Google Scholar, ERIC and Science Direct). The collected literature was reviewed thematically. The literature indicated that virtual learning is the useful learning process and an opportunity for higher education as well as school level to continue formal education from home, although it has many challenges. Although there are fewer number of studies on the virtual learning environment in Mathematics, some studies emphasise combined use of virtual manipulative and physical manipulative to increase the mathematical ability. Also, some literature indicates that online learning is more effective than traditional classroom learning but the rate of completion online mathematics course is lower than the classroom learning.

A study on pre-service mathematics teachers’ criteria of proof evaluation

Proof is foundational to mathematics, and constructing proofs and establishing their validity are both important mathematical studies. Determining the validity of a proof is a part of the process of proof evaluation. Proof evaluation contributes to students’ ability to construct and revise their own proofs. The purpose of this study was to determine the criteria pre-service mathematics teachers take into account in evaluating a proof. The study was carried out with 50 first-year university students enrolled in an elementary mathematics teacher education program. The data were collected through activities relating to proving. The results of this study revealed that, when evaluating a proof, the participants regarded use of appropriate definitions, axioms, or theorems in the steps of the proof as the most important criterion with reference to justification, while in terms of mathematical language; they regarded appropriate use of symbolic language as the most important criterion. However, they tended to ignore situations where non-symbolic language was used. To address this issue, it is recommended that mathematics-learning environments include the use of non-symbolic language, as well as symbolic representations, in the definition of mathematical concepts.

Students' Understanding of Mathematical Concepts in terms of Emotional and Spatial Intelligence

Conceptual understanding is one of the core standards in mathematics or as a key component of mathematical skills. Understanding mathematical concepts is knowledge that involves a thorough understanding of the underlying concepts and the basis behind the algorithms performed in mathematics. A student must have this understanding if he wants to understand mathematics in depth. The problem may not be because it is solely related to the learning process, but rather the internal intelligence of students. This study examines how the relationship between spatial and emotional intelligence with students' understanding of mathematical concepts. This research is a correlational research with multiple correlation research design. This research involved 66 students of SMP class VIII in Kab. East Manggarau, NTT as a sample. Data collection is done by using questionnaires and tests. Before the data were analyzed correlatively, both simple and multiple, the analysis prerequisite tests were carried out, namely normality, linearity, and multicollinearity. The results of data analysis show that these three test requirements are met and the results of hypothesis testing indicate that there is a positive and significant relationship between emotional and spatial intelligence and students' understanding of mathematical concepts (either partially or simultaneously). Simultaneously, these two intelligences contribute 16.08% to increasing students' understanding of mathematical concepts. The study provides a recommendation that in improving students' understanding of mathematical concepts, consideration of students' basic intelligence factors needs to be considered before being treated or designing a mathematics learning environment

How Do We Learn Mathematics A Framework for a Theoretical and Practical Model

The purpose of this paper is to propose an effective learning environment for the initial stages of mathematical learning. Basic numerical skills and the objects and actions that trigger those skills are conceptualized as a mathematics-learning environment. We discuss numerical learning mechanism and the basic skills and environments we use to learn numbers briefly within the human cognition system. The three subsystems of number, i.e., exact number system, approximate number system and access to symbol system, are explained with reference to basic number competencies. They are discussed within the framework of "number sense” by drawing evidences from the neuroscience and mathematics education literature. Finally, how to manipulate the components of these subsystems for an effective learning of number is exemplified in a proposed model of mathematical learning environment.

Evaluating students' engagement with an online learning environment during and after COVID-19 related school closures: A survival analysis approach.

BackgroundDue to the COVID-19 pandemic schools all over the world were closed and thereby students had to be instructed from distance. Consequently, the use of online learning environments for online distance learning increased massively. However, the perseverance of using online learning environments during and after school closures remains to be investigated.MethodWe examined German students’ (n ≈ 300,000 students; ≈ 18 million computed problem sets) engagement in an online learning environment for mathematics by means of survival analysis.ResultsWe observed that the total number of students who registered increased considerably during and after school closures compared to the previous three years. Importantly, however, the proportion of students engaged also decreased more rapidly over time.ConclusionThe application of survival analysis provided valuable insights into students’ engagement in online learning - or conversely students’ increased dropout rates - over time. Its application to educational settings allows to address a broader range of questions on students’ engagement in online learning environments in the future.

Exploring the Pros and Cons of Implementing Flipped Classroom in a Virtual Learning Environment in Mathematics 7

Effective implementation of virtual learning has been a challenge encountered by many teachers. This paper investigates the experiences of twenty (20) grade seven students from a university exposed to virtual learning using the flipped classroom model in Mathematics. The informants were chosen from eight learning groups (LG) enrolled in online learning from 2020-2021. The study employed a case study design and used the Clarke and Braun thematic analysis (TA) approach to interpret the qualitative data. It used individual interviews, focused group discussions (FGD), and interviews with parents and teachers to collect relevant information. Google Meet was used to gather the data needed. This study aims to address the challenges encountered by the implementation of virtual classes during the pandemic. It also seeks to explore the pros and cons of putting the flipped classroom approach into practice in a virtual learning environment. The findings revealed that the flipped classroom approach could be an effective strategy in enhancing students’ positive attributes toward learning and socialization in an online learning environment. Also, the teacher could transform the teaching and learning process into a more student-centered classroom in which assessment could be carried out effectively. For future purposes, researchers could address the cons of this study by integrating anecdotal records and performance trackers into the new flipped classroom model developed.